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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2510.20481 |
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| _version_ | 1866908607107301376 |
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| author | Goff, Théotime Le Devijver, Émilie |
| author_facet | Goff, Théotime Le Devijver, Émilie |
| contents | Out-of-distribution generalization is key to building models that remain reliable across diverse environments. Recent causality-based methods address this challenge by learning invariant causal relationships in the underlying data-generating process. Yet, measuring how causal structures differ across environments, and the resulting generalization difficulty, remains difficult. To tackle this challenge, we propose the Structural Causal Model Distance (SCMD), a principled metric that quantifies discrepancies between two SCMs by combining (i) kernel-based distances for nonparametric comparison of distributions and (ii) pairwise interventional comparisons to capture differences in causal effects. We show that SCMD is a proper metric and provide a consistent estimator with theoretical guarantees. Experiments on synthetic and real-world datasets demonstrate that SCMD effectively captures both structural and distributional differences between SCMs, providing a practical tool to assess causal transferability and generalization difficulty. Given two joint distributions P 1 (V j ) and P 2 (V j ), the Maximum Mean Discrepancy (MMD, Gretton et al. which defines a metric between distributions for characteristic kernels (Fukumizu et al., 2007). Kernel conditional mean embeddings (Park and Muandet, 2020) represent conditional expectation operators in an RKHS H Vj , which allows us to define the Maximum Conditional Mean Discrepancy between two |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20481 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SCMD: A Kernel-Based Distance for Structural Causal Models to Quantify Transferability Across Environments Goff, Théotime Le Devijver, Émilie Statistics Theory Out-of-distribution generalization is key to building models that remain reliable across diverse environments. Recent causality-based methods address this challenge by learning invariant causal relationships in the underlying data-generating process. Yet, measuring how causal structures differ across environments, and the resulting generalization difficulty, remains difficult. To tackle this challenge, we propose the Structural Causal Model Distance (SCMD), a principled metric that quantifies discrepancies between two SCMs by combining (i) kernel-based distances for nonparametric comparison of distributions and (ii) pairwise interventional comparisons to capture differences in causal effects. We show that SCMD is a proper metric and provide a consistent estimator with theoretical guarantees. Experiments on synthetic and real-world datasets demonstrate that SCMD effectively captures both structural and distributional differences between SCMs, providing a practical tool to assess causal transferability and generalization difficulty. Given two joint distributions P 1 (V j ) and P 2 (V j ), the Maximum Mean Discrepancy (MMD, Gretton et al. which defines a metric between distributions for characteristic kernels (Fukumizu et al., 2007). Kernel conditional mean embeddings (Park and Muandet, 2020) represent conditional expectation operators in an RKHS H Vj , which allows us to define the Maximum Conditional Mean Discrepancy between two |
| title | SCMD: A Kernel-Based Distance for Structural Causal Models to Quantify Transferability Across Environments |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2510.20481 |